I seriously doubt syslog-ng would get a nice SIGHUP in case of a crash (or even when doing a hard-reboot for that matter), so syslog-ng probably hasn't much to do with the crashes
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It's probably just coincidental that it happened soon after a log rotation, that's all.
And it's quite possible that in case of a crash, you wouldn't see anything in the logs, because the system crashed before the syslog could dump its buffer in the actual logfile (In which case the only way to actually see an up to date log would be via a live terminal, either a remote shell or a serial console).
The syslog-ng starting & kernel bootlog is a normal boot log output, the 'new configuration initialized' msg is specific to the SIGHUP signal, because that's the point of this signal, making the daemon reload the config (because it changed, or in a case of a syslog, to avoid losing logs because an external tool rotated the logfiles [tinyrot in the Kindle case]).